The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a novel transit radio telescope operating across the 400-800-MHz band. CHIME is comprised of four 20-m x 100-m semi-cylindrical paraboloid reflectors, each of which has 256 dual-polarization feeds suspended along its axis, giving it a >200 square degree field-of-view. This, combined with wide bandwidth, high sensitivity, and a powerful correlator makes CHIME an excellent instrument for the detection of Fast Radio Bursts (FRBs). The CHIME Fast Radio Burst Project (CHIME/FRB) will search beam-formed, high time-and frequency-resolution data in real time for FRBs in the CHIME field-of-view. Here we describe the CHIME/FRB backend, including the real-time FRB search and detection software pipeline as well as the planned offline analyses. We estimate a CHIME/FRB detection rate of 2-42 FRBs/sky/day normalizing to the rate estimated at 1.4-GHz by Vander Wiel et al. (2016). Likely science outcomes of CHIME/FRB are also discussed. CHIME/FRB is currently operational in a commissioning phase, with science operations expected to commence in the latter half of 2018.